Joins of Projective Varieties: A Cancellation Theorem for Curves

Abstract

Let X, Y, Z be integral subvarieties of P ⁿ . Let [X; Y] ⊆  P ⁿ denote the join. Under what conditions on X, Y and/or Z if [X; Y] = [X; Z], then Y = Z? Here, we study the case in which X, Y and Z are curves.

Key Words:

• Joins of projective varieties
• Join
• Cancellation problem

Acknowledgment

The author was partially supported by MIUR and GNSAGA of INdAM (Italy).

Notes

^#Communicated by L. Ein.